(a) Answer ( y − 2 ) 2 = ± 8 ( x + 3 ) Explanation Given information: Critical Thinking: The Latus rectum of a parabola is the line segment through the focus that is perpendicular to the axis has endpoints on the parabola. The length of the latus rectum is | 4 p | units, where p is the distance from the vertex to the focus. Calculation: The vertex and axis give us the base formula: ( y − 2 ) 2 = 4 p ( x + 3 ) | 4 p | = 8 → p = ± 2 This gives us 2 options: ( y − 2 ) 2 = ± 8 ( x + 3 ) (b) To determine To write: The equation of the circle, if the latus rectum of the parabola with equation ( x − 1 ) 2 = − 16 ( y − 4 ) coincides with the diameter of a circle. Answer ( x − 1 ) 2 + y 2 = 64 Explanation Given information: Critical Thinking: The Latus rectum of a parabola is the line segment through the focus that is perpendicular to the axis has endpoints on the parabola. The length of the latus rectum is | 4 p | units, where p is the distance from the vertex to the focus. Calculation: 4 p = − 16 | 4 p | = | − 16 | Since the vertex of the parabola is ( 1 , 4 ) and downward facing, this puts the center of the circle at ( 1 , 0 ) Since the latus rectum is 16 long, this makes the radius of the circle 8. This gives the equation: ( x − 1 ) 2 + y 2 = 64

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Question

Chapter 10.5, Problem 38E

(a)

To determine

To write: The equation of a parabola with vertex at (−3,2), axis y = 2 and latus rectum 8 units long.

(a)

Expert Solution

Answer to Problem 38E

(y−2)2=±8(x+3)

Explanation of Solution

Given information: Critical Thinking: The Latus rectum of a parabola is the line segment through the focus that is perpendicular to the axis has endpoints on the parabola. The length of the latus rectum is |4p| units, where p is the distance from the vertex to the focus.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.5, Problem 38E , additional homework tip 1

Calculation:

The vertex and axis give us the base formula:

(y−2)2=4p(x+3)|4p|=8→p=±2

This gives us 2 options:

(y−2)2=±8(x+3)

(b)

To determine

To write: The equation of the circle, if the latus rectum of the parabola with equation (x−1)2=−16(y−4) coincides with the diameter of a circle.

(b)

Expert Solution

Answer to Problem 38E

(x−1)2+y2=64

Explanation of Solution

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.5, Problem 38E , additional homework tip 2

Calculation:

4p=−16|4p|=|−16|

Since the vertex of the parabola is (1,4) and downward facing, this puts the center of the circle at (1,0)

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.5, Problem 38E , additional homework tip 3

Since the latus rectum is 16 long, this makes the radius of the circle 8.

This gives the equation:

(x−1)2+y2=64

Chapter 10.5, Problem 37E

Chapter 10.5, Problem 39E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY

The equation of a parabola with vertex at ( − 3 , 2 ) , axis y = 2 and latus rectum 8 units long.

Concept explainers

Videos

To write: The equation of a parabola with vertex at (−3,2), axis y = 2 and latus rectum 8 units long.

Answer to Problem 38E

Explanation of Solution

To write: The equation of the circle, if the latus rectum of the parabola with equation (x−1)2=−16(y−4) coincides with the diameter of a circle.

Answer to Problem 38E

Explanation of Solution

Chapter 10 Solutions

Additional Math Textbook Solutions